Thermodynamics of spin S=1/2 antiferromagnetic uniform and alternating-exchange Heisenberg chains

Journal Article · Sat Apr 01 04:00:00 EST 2000 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/PhysRevB.61.9558· OSTI ID:20215836

Johnston, D C ^[1]; Kremer, R K ^[2]; Troyer, M ^[3]; Wang, X ^[4]; Kluemper, A ^[5]; Bud'ko, S L ^[1]; Panchula, A F ^[1]; Canfield, P C ^[1]

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1. Ames Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011 (United States)
2. Max-Planck-Institut fuer Festkoerperforschung, Heisenbergstrasse 1, Postfach 800665, D-70569 Stuttgart, (Germany)
3. Institute for Solid State Physics, University of Tokyo, Roppongi 7-22-1, Tokyo 106, (Japan)
4. Institut Romand de Recherche Numerique en Physique des Materiaux, IN-Ecublens, CH-1015 Lausanne, (Switzerland)
5. Universitaet zu Koeln, Institut fuer Theoretische Physik, Zuelpicher Strasse 77, D-50937, (Germany)

The magnetic susceptibility {chi}{sup *}(t) and specific heat C(t) versus temperature t of the spin S=1/2 antiferromagnetic (AF) alternating-exchange (J{sub 1} and J{sub 2}) Heisenberg chain are studied for the entire range 0{<=}{alpha}{<=}1 of the alternation parameter {alpha}{identical_to}J{sub 2}/J{sub 1} (J{sub 1}, J{sub 2}{>=}0, J{sub 2}{<=}J{sub 1}, t=k{sub B}T/J{sub 1}, {chi}{sup *}={chi}J{sub 1}/Ng{sup 2}{mu}{sub B}{sup 2}). For the uniform chain ({alpha}=1), the high-accuracy {chi}{sup *}(t) and C(t) Bethe ansatz data of Kluemper and Johnston (unpublished) are shown to agree very well at low t with the respective exact theoretical low-t logarithmic correction predictions of Lukyanov [Nucl. Phys. B 522, 533 (1998)]. Accurate ({approx}10{sup -7}) independent empirical fits to the respective data are obtained over t ranges spanning 25 orders of magnitude, 5x10{sup -25}{<=}t{<=}5, which contain extrapolations to the respective exact t=0 limits. The infinite temperature entropy calculated using our C(t) fit function is within 8 parts in 10{sup 8} of the exact value ln 2. Quantum Monte Carlo (QMC) simulations and transfer-matrix density-matrix renormalization group (TMRG) calculations of {chi}{sup *}({alpha},t) are presented for 0.002{<=}t{<=}10 and 0.05{<=}{alpha}{<=}1, and an accurate (2x10{sup -4}) two-dimensional ({alpha},t) fit to the combined data is obtained for 0.01{<=}t{<=}10 and 0{<=}{alpha}{<=}1. From the low-t TMRG data, the spin gap {delta}({alpha}) is extracted for 0.8{<=}{alpha}{<=}0.995 and compared with previous results, and a fit function is formulated for 0{<=}{alpha}{<=}1 by combining these data with literature data. We infer from our data that the asymptotic critical regime near the uniform chain limit is only entered for {alpha}(greater-or-similar sign)0.99. We examine in detail the theoretical predictions of Bulaevskii [Sov. Phys. Solid State 11, 921 (1969)], for {chi}{sup *}({alpha},t) and compare them with our results. To illustrate the application and utility of our theoretical results, we model our experimental {chi}(T) and specific heat C{sub p}(T) data for NaV{sub 2}O{sub 5} single crystals in detail. The {chi}(T) data above the spin dimerization temperature T{sub c}{approx_equal}34 K are not in quantitative agreement with the prediction for the S=1/2 uniform Heisenberg chain, but can be explained if there is a moderate ferromagnetic interchain coupling and/or if J changes with T. Fitting the {chi}(T) data using our {chi}{sup *}({alpha},t) fit function, we obtain the sample-dependent spin gap and range {delta}(T=0)/k{sub B}=103(2) K, alternation parameter {delta}(0)(ident to)(1-{alpha})/(1+{alpha})=0.034(6) and average exchange constant J(0)/k{sub B}=640(80) K. The {delta}(T) and {delta}(T) are derived from the data. A spin pseudogap with magnitude {approx_equal}0.4{delta}(0) is consistently found just above T{sub c}, which decreases with increasing temperature. From our C{sub p}(T) measurements on two crystals, we infer that the magnetic specific heat at low temperatures T(less-or-similar sign)15 K is too small to be resolved experimentally, and that the spin entropy at T{sub c} is too small to account for the entropy of the transition. A quantitative analysis indicates that at T{sub c}, at least 77% of the entropy change due to the transition at T{sub c} and associated order parameter fluctuations arise from the lattice and/or charge degrees of freedom and less than 23% from the spin degrees of freedom. (c) 2000 The American Physical Society.

• OSTI ID: 20215836
• Journal Information: Physical Review. B, Condensed Matter and Materials Physics, Journal Name: Physical Review. B, Condensed Matter and Materials Physics Journal Issue: 14 Vol. 61; ISSN 1098-0121
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ANTIFERROELECTRIC MATERIALS
ANTIFERROMAGNETIC MATERIALS
CHAINS
ELECTRON EXCHANGE
ENERGY GAP
ENTROPY
EXCHANGE INTERACTIONS
EXPERIMENTAL DATA
HEISENBERG MODEL
MAGNETIC SUSCEPTIBILITY
MONTE CARLO METHOD
SIMULATION
SPECIFIC HEAT
SPIN
TEMPERATURE RANGE 0013-0065 K
TEMPERATURE RANGE 0065-0273 K
THEORETICAL DATA
THERMODYNAMICS